Resistance of superconducting nanowires connected to normal-metal leads

We study experimentally the low temperature resistance of superconducting nanowires connected to normal metal reservoirs. We find that a substantial fraction of the nanowires is resistive, down to the lowest temperature measured, indicative of an intrinsic boundary resistance due to the Andreev-conversion of normal current to supercurrent. The results are successfully analyzed in terms of the kinetic equations for diffusive superconductors.

Figure 1

SEM picture of a device (slightly misaligned), showing the coverage of the thin aluminium film with the thick $\mathrm{Cu}$ layer (except for one the measured devices are carefully lined up). The inset shows a schematic picture of an ideal device.

Figure 2

(Color online) Measured $R–T$ curves for four different bridge lengths. The intrinsic $T_{c0}$ is indicated by the vertical dashed line. The inset shows the measured critical temperature of the wire versus $1∕L^2$, which is used to determine $T_{c0}$ by letting $L\to \infty$.

Figure 3

The calculated density-of-states $N_1$ at various distances from the reservoirs $\left(x=100,200,300,400,500,1000\mathrm{nm}\right)$ for a $2\mu \mathrm{m}$ long wire ($t=0.4$, $D=160{\mathrm{cm}}^2∕\mathrm{s}$, and ${\Delta }_0=192\mu \mathrm{eV}$). Note the exponentially small but finite subgap density-of-states in the middle (at $x=1\mu \mathrm{m}$; see inset).

Figure 4

The voltage in the superconducting wire as a function of position for two different temperatures ($t=0.4$ and $0.9$). At $t=0.9$ the wire behaves as a normal metal and for $t=0.4$ the voltage is clearly present to a depth $\xi$ (wire length $2\mu \mathrm{m}$ with $D=160{\mathrm{cm}}^2∕\mathrm{s}$ and ${\Delta }_0=192\mu \mathrm{eV}$). The inset shows the position dependent normal currents and supercurrents.

Figure 5

(Color online) The measured $R–T$ curve for the $2\mu \mathrm{m}$ bridge together with the model calculation using the boundary condition $\theta (x=0,L)=0$ (dots), and using the boundary condition ${\partial }_x\theta (x=0,L)=\theta (x=0,L)∕a$ (triangles) with $a=75\mathrm{nm}$. The value for $T=0$ is 0.3255 for the hard boundary conditions (dots), and 0.2609 for the soft boundary conditions.